The day before, make the cheesecake. Preheat the oven to 350 degrees and bring a kettle of water to a boil. Grease a 10-inch springform pan with cooking spray. Sprinkle with sugar, tapping out excess. Wrap foil around the outside of the pan so it comes up the sides (this prevents the water bath from seeping into the cake).
In an electric mixer, beat the yogurt, mascarpone, sugar and confectioner's sugar on medium speed until smooth, about 1 minute. Beat in the eggs and egg yolks, one at a time, scraping down the sides. Beat in the salt and vanilla.
Transfer to the springform and set it in a large roasting pan. Fill the roasting pan with enough hot water to rise halfway up the springform. Cover the roasting pan with foil, tenting the foil so it does not touch the cheesecake. Bake for 20 minutes. Rotate the pan and bake for 20 minutes more. Uncover and continue baking, until the cake is puffed but not cracked, jiggly but not liquid in the center, for about 25 minutes more.
Cool cake in the roasting pan until the water is lukewarm, then cool on a rack.
Cover and refrigerate overnight. Remove sides from springform and serve.